value of integration , Mathematics

Assignment Help:

what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n

Solution)  limit n-->inf.    [1 + (n!-n^n)/n^n]^1/n

= e^ limit n-->inf.    {(n!-n^n)/n^n}.1/n         

                             (applying formula lim x-->a  [1 + f(x)]^g(x) =    e ^ {lim x-->a    f(x).g(x)}  )

=e ^ lim n-->inf.       (n-1)!/(n)^n-1   -   1/n

=e ^ lim n---> inf.     (1-1/n)(1-2/n)(1-3/n)......1/n   -    1/n

=e ^ (1-o)(1-0).....(1-0).0  -   0

=e ^ 0-0

=1

hence, integation 1= x + C

 

 


Related Discussions:- value of integration

Problem solver, a bathroom measure 250 cm by 175 cm calculate the side of t...

a bathroom measure 250 cm by 175 cm calculate the side of the largest square tile that can tile the floor

Find and classify the differential equation, Find and classify the equilibr...

Find and classify the equilibrium solutions of the subsequent differential equation. y' = y 2 - y - 6 Solution The equilibrium solutions are to such differential equati

Mean deviation, is that formula of sample and population for mean deviation...

is that formula of sample and population for mean deviation is the same?

Earth geometry, calculate the shortest distance between A and B 40degrees w...

calculate the shortest distance between A and B 40degrees west and 50 degrees east respectively laying along 57 degrees north

Sketch the parametric curve for parametric equations, Sketch (draw) the par...

Sketch (draw) the parametric curve for the subsequent set of parametric equations. x = t 2 + t y = 2t -1 Solution At this point our simply option for sketching a par

Theory of numbers, show that all primes except 2, are of the form 4n-1 or 4...

show that all primes except 2, are of the form 4n-1 or 4n+1

Negative skewness-measure of central tendency, Negative Skewness It i...

Negative Skewness It is an asymmetrical curve whether the long tail extends to the left NB: In developed countries this frequency curve for the age distribution is charact

Explain the graph of an equation and graph of an inequality, Explain The Gr...

Explain The Graph of an Equation and The Graph of an Inequality ? Here is the graph of the equation y = x. Notice that for every point along the line shown in the graph, the y

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd